The effect of apathy and compulsivity on planning and stopping in sequential decision-making

Real-life decision-making often comprises sequences of successive decisions about whether to take opportunities as they are encountered or keep searching for better ones instead. We investigated individual differences related to such sequential decision-making and link them especially to apathy and compulsivity in a large online sample (discovery sample: n = 449 and confirmation sample: n = 756). Our cognitive model revealed distinct changes in the way participants evaluated their environments and planned their own future behaviour. Apathy was linked to decision inertia, i.e., automatically persisting with a sequence of searches for longer than appropriate given the value of searching. Thus, despite being less motivated, they did not avoid the effort associated with longer searches. In contrast, compulsivity was linked to self-reported insensitivity to the cost of continuing with a sequence of searches. The objective measures of behavioural cost insensitivity were clearly linked to compulsivity only in the discovery sample. While the confirmation sample showed a similar effect, it did not reach significance. Nevertheless, in both samples, participants reported awareness of such bias (experienced as “overchasing”). In addition, this awareness made them report preemptively avoiding situations related to the bias. However, we found no evidence of them actually preempting more in the task, which might mean a misalignment of their metacognitive beliefs or that our behavioural measures were incomplete. In summary, individual variation in distinct, fundamental aspects of sequential decision-making can be linked to variation in 2 measures of behavioural traits associated with psychological illness in the normal population.

Parameter recovery (schedule used for confirmation sample). The  table  shows correlations (Pearson's r) between simulated ('ground truth') parameters (headers highlighted in grey) and the fitted ('recovered') parameters (headers with white background) for the decision models of the initial (top) and later (bottom) searches. All parameters showed very good recovery (r>0.88, diagonal, highlighted in blue). The off-diagonal values show that confusion between parameters was very low (all < 0.22). We used 500 simulated participants for these results. Data in files 13 and 14.  Table B. Parameter correlations for initial decisions (confirmation sample). We ran a pearson correlation of the hierarchically fit parameter estimates from our cognitive model on the initial decisions to look at their relationships. Even though simulations (table S1) showed very low parameter confusions, parameters from real participants showed in parts substantial correlations (Pearson's r), suggesting those correlations are a real relationship existing in participants, rather than an artifact of model fitting. invTemp (inverse temperature of the softmax equation linking value to choice probabilities), SearchBias (bias for or against searching). Prospective (prospective value of the model), Myopic (Myopic value of the model). AvgProspVChange (average change of prospective value per search in the future). Data in file 11.   [7], Toronto alexithymia scale [8]. Depression cut offs were (less than 13 'Minimal', less then 20 'Mild', less than 29 'Moderate' and higher or equal 29 'Severe'). Obsessive-compulsion less than 21 'none', otherwise 'clinically significant'). For social anxiety we had less than 30 as 'none', between 30 but less than 60 as 'possible' and at and above 60 as 'probable' social anxiety. For Alexithymia we had less than 52 as none, between 52 but less than 61 as 'possible' and at and above 62 as 'present' Alexithymia. Fatigue was 'none' below 22, 'present' between 22 and 34 and 'extreme' above 34. Data in file 5.     Table I: Additional medication information (confirmation sample). All information for the types of medications excluded and included participants used (NO and Yes). The most common medication were selective serotonin reuptake inhibitor. Data in file 6.

Decision tree model to derive prospective value
As the decision tree model is identical to a previous paper [9] we include the model description from there: " The aim of the model is to compute the value of searching taking into account the possibility for future searches given the current search horizon (available number of searches), the alternatives' properties, and search costs.  […]. Note, the model also employs a changing acceptance-thresholds at each search step; it allows for different p(Search)and p(Accept) for every step in the sequence (or level of the tree; fig.S1B). The term s corresponds to the search number within the tree (e.g. s=1 is the first search in an environment). " [9]. See also the previous paper [9], supplements figure S1 for a visualization of the model.

Task schedule design and model validation
When designing the task schedules for the confirmation sample, we ensured that it would allow us to reliably measure participants' behaviour. Specifically, this was achieved by generating random schedules (given the constraint for variables such as number of trials and levels of cost as detailed in the methods of the main text). We then simulated choices of 500 participants given random combinations of model parameters within the ranges of those found for the real participants of the discovery sample.
We then analysed these simulated choices with the same decision models as for the real participants. The only difference was that we did not use a hierarchical model and that the model was fit using Stan's Variational Bayes algorithm, rather than sampling to increase speed of the procedure. The reason we used a non-hierarchical model to fit the simulated data was because parameter combinations were drawn with a flat distribution in the ranges of real participants, rather than following a normal distribution. We then checked, for both types of analyses (i.e. first choice and later choices on each trial separately) that the correlations between the simulated ('ground truth') and the fitted parameters were r>0.7 (see figure S5). If a schedule did not fulfil these criteria it was abandoned and a new schedule was created.
As a technical aside, we found that the most reliable way to simulate the data was to z-score the variables before scaling them by each simulated subject's parameters -for the analysis of the first search -exactly as was done with the real data. For the analysis of the later searches this was not possible as what offers simulated participants would encounter would depend on their choices (e.g. if they did not search on search 1 of trial 1, there would of course be no 'later searches' for that trial). Therefore, we instead standardized the variables using the mean and standard deviation from the discovery sample. The checks of the correlations between simulated and real described above only ensure consistency of the parameter values within a given schedule. It is possible that across schedules there is no such consistency; for example, let's assume a simulated parameter is in the range 0 to 1 and in schedule A recovers with r=0.8 in the range 0 to 1 and in schedules B recovers with r=0.8 in the range of 1 to 2. Then the overall parameter recovery across schedules would be bad. Thus, we combined data from all simulated participants across all schedules and checked the correlations, again as r>0.7.
To check how well our decision model fitted our data, we computed the negative log likelihood for each measurement from each participant using a half-split cross-validation procedure. Specifically, for each participant we selected a random half of their data points and then fitted hierarchical models to these 'training data'. We then applied the parameters to the 'test data' (remaining half of data) and computed for each data point the fit (negative log likelihood). As a cross-validation procedure was used, no further adjustment for the number of model parameters was needed. We compared models that contained all regressors of interest, as well as control regressors (see figure S2A), with models where iteratively one of the regressors was removed (figure S2C). The aim was to test how important each of the regressors was for capturing participants' behaviour. We compared the model fit by computing the sum of the negative log likelihoods across participants, lower values suggest better fit.

SUPPLEMENTARY RESULTS
We analysed the behavioural data with cognitive models based on our previous paper [9]. This was done separately for the initial search decision on each trial and for the later decisions on each trial. In short, we analysed two different kinds of measurements during the decisions. Firstly, we looked at the choice pattern and secondly RT, to test choice preference and deliberation i.e. what participants paid attention to, how long for, and when. Of key clinical interest here are three facets of the task. First, there is a behavioural measure of decision inertia, i.e. a 'stuck in a rut' bias. Second, it is possible to measure insensitivity to costs during a sequence of searches. Third, it is possible to examine 'preemptive avoidance' that occurs at the beginning of the sequence and which is aimed at preventing the bad consequences of such biases when they occur later in the sequence. We will first describe how the behavioural measures are derived from the task. Then we will describe how we have related the cognitive task as well as introspective measures to clinical measures of apathy and compulsivity.

Planning and initiating a search sequence
As previously [9], when deciding whether to accept the default (initial offer) or spin, participants took into account all information that they rationally should (figure S1, results obtained using a decision model using an approach analogous to a logistic regression analysis, see methods 'Analysisdecision'): Participants were more likely to accept the initial offer right away rather than initiate a search, the higher its value (mean=-0.33, 95% CI [-0.33--0.32]) and the more costly it was to spin the wheel (mean=-0.08, 95% CI [-0.08--0.07]). In contrast, participants were more likely to search when the average value of the alternatives was high (we refer to this as the myopic value as it only represents the average value of the next search) (mean=0.25, 95% CI [0.25-0.26]). They were also more likely to search the higher the 'prospective value' (mean=0.05, 95% CI [0.05-0.06]), i.e. the value derived from planning ahead (see supplements section 'Decision tree model' for details on derivation of the prospective value; intuitively, prospective value reflects the additional value that stems from the fact that one can choose to reject bad offers and search again, rather than being stuck with the first offer one gets).
We also found that participants tried, pre-emptively, to avoid situations in which they were subsequently likely to express decision-inertia or insensitivity to cost of searching when performing the sequence of searches (see below, figure S2). To demonstrate this, we first created a measure that captured for each trial how rapidly participants needed to adjust their search strategy as they proceeded through a sequence (AvgProspVChange, i.e. how much the prospective value changes per future search, see methods for details]). The faster the value of searching decreases (i.e. the faster the search strategy needs to be changed), the more expensive later biases are. Thus, if you are aware of your own biases, you should, pre-emptively, particularly avoid starting the search sequence on such trials. This is indeed what we found (mean=-0.03, 95% CI [-0.03 --0.02]), figure S1A). Relatedly, about half of the participants also self-reported that they pre-emptively avoided trials on which they thought they might over-persevere (figure S1C). We find (see figure 5D, main text) a strong relationship between another sequential bias (cost insensitivity) and self-reported pre-emptive avoidance that is mediated by awareness. Furthermore, our large confirmation sample will give more conclusive evidence about the exact relationship between the many possible biases and their pre-emption in our task, as we could now prespecify the exact relationships to test.

Carrying out a choice sequence
After initiating a search sequence, participants made a series of decisions of either banking an offer (and ending the trial) or searching again (as shown in Figure 2 in main manuscript). We can assess, using the same kind of computational model as above (methods section 'Analysis -decision'), whether participants behave mostly rationally and also whether they have decision inertia, i.e. show a 'stuck in the rut' bias. As before and as they should rationally, we find (figure S2A) that participants are more likely to go on searching if the myopic value is high (mean=0.26, 95% CI [0.26 -0.26]), if the prospective value is high (mean=0.07, 95% CI [0.07 -0.07]) or if the cost of searching is low (mean=-0.08, 95% CI [-0.08 --0.08]) or if the drawn offers are low (mean=-0.49, 95% CI [-0.49 --0.48]) . We however also find evidence for decision inertia ('stuck in a rut' bias): the more participants had already searched, the more likely they were to search again (mean=0.04, 95% CI [0.03 -0.04]). Using our computational model, we could in fact dissociate this from other alternative explanations of searching too often. One possibility might have been that participants only compute the prospective value of a trial once in the beginning of a trial. Then, as they go through as sequence, they would not take into account that as they go through a sequence of searches they must adjust their prospective value because as fewer searches remain there are fewer opportunities to encounter good offer and reject bad ones. However, we find that participants in fact adjust their prospective value ('ProspVS1-Adapted', mean=-0.03, 95% CI [-0.04 --0.03]). Another possibility might have been -and which is what we assumed previouslythat participants have a sunk cost fallacy, i.e. that they are more likely to continue searching the more costs they've already paid on a trial. However this was not the case ('TotalCost' is not positive, (mean=-0.00, 95% CI [-0.00 --0.00]). In terms of subjective experience, participants reported both 'decision inertia', i.e. searching too often just because they had already searching (about half of the participants, figure S2C) and 'over chasing' of alternatives, i.e. searching too often because an alternative on the wheel appeared particularly appealing, (figure S2D).